Question

Найди значение выражения

7c/c^2−n^2 + 7/ n−c
при
c = −3,
n = −1.

Пример 2

10с/с^2-n^2+10/n-c

при

с = -3 ,

n = -1

Answer 1

$1) \ \dfrac{7c}{c^{2} -n^{2} }+\dfrac{7}{n-c} =\dfrac{7c}{(c-n)(c+n)}-\dfrac{7}{c-n}=\dfrac{7c-7c-7n}{(c-n)(c+n)}=\dfrac{7n}{n^{2}-c^{2}} \\\\\\c=-3 \ ; \ n=-1\\\\\\\dfrac{7n}{n^{2}-c^{2}}=\dfrac{7\cdot(-1)}{(-1)^{2}-(-3)^{2}}=\dfrac{-7}{1-9}=\dfrac{-7}{-8}=\boxed{0,875}$

$2) \ \dfrac{10c}{c^{2}-n^{2}}+\dfrac{10}{n-c}=\dfrac{10c}{(c-n)(c+n)} -\dfrac{10}{c-n}=\dfrac{10c-10c-10n}{(c-n)(c+n)}=\dfrac{10n}{n^{2}-c^{2}} \\\\\\c=-3 \ ; \ n=-1\\\\\\\dfrac{10n}{n^{2}-c^{2}}=\dfrac{10\cdot(-1)}{(-1)^{2}-(-3)^{2}}=\dfrac{-10}{1-9}=\dfrac{-10}{-8}=\boxed{1,25}$